The end links on the 116519 Daytona fit into slots in the case and
the bezel is pressure fit on top to keep them in place. Those 2 watches
have entirely different cases, although they don't look very different.

You can take the bracelet off a 116509 and put a strap on it, but there will
be a space between the strap end and the case. There are aftermarket end links
( I think my friend Will has a pair ), but I've only seen them in steel. I am
certain a capable goldsmith can custom make you a pair, but they will not be
like the strap model that fits into the case- they simply mount over the pins.
But I have seen them on steel Daytonas and they look great!

It can be done but very fidgety and you need to confident with the removal of the bezel. Not easy but can be done. You cannot put end links on a bracelet Daytona as per the strap versions. But as LarryK said a custom version is possible.

"A dry Martini," he said. "One. In a deep champagne goblet."
"Oui, monsieur."
"Just a moment. Three measures of Gordon's, one of vodka, a half measure of Kina Lillet. Skake it very well until it's ice cold, then add a large thin slice of lemon-peel. Got it?" - JB
- Ian Fleming, Casino Royale (1953).